We have all observed that offspring tend to have physical traits in common with their parents. In humans, similarity in hair color, eye color, height, and build often quite clearly run in families. That selective breeding might enhance traits must have been noticed long ago in our history, as domesticated animals and crops have strongly developed features that we find useful.

On the other hand, the traits of offspring are generally not completely predictable from observing those of the parents. A child might have a trait, such as hemophilia, that neither parent exhibits, though such a trait might occur more commonly within one family than another. Thus, despite patterns to inheritance, chance also appears to be involved. Creating a mathematical model of heredity requires capturing both of these aspects.

The first decisive step was taken by the Augustinian monk Gregor Mendel in the latter half of the nineteenth century. Experimenting with some carefully chosen traits in peas, he was led to propose what we now call a gene as the basic unit of inheritance. Though it is perhaps surprising to the modern student, at that time the gene was an entirely abstract concept, with no proposed physical basis, such as the DNA sequences we now immediately imagine.

Recognizing the value of quantitative analysis, Mendel created a mathematical model for the transmission of heritable traits, based on the concepts of probability.